Example 20 - Chapter 9 Class 12 Differential Equations
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 20 Find the particular solution of the differential equation log(๐๐ฆ/๐๐ฅ)=3๐ฅ+4๐ฆ given that ๐ฆ=0 ๐คโ๐๐ ๐ฅ=0 log(๐๐ฆ/๐๐ฅ)=3๐ฅ+4๐ฆ ๐ ๐/๐ ๐ = e(3x + 4y) ๐๐ฆ/๐๐ฅ = e3x e4y Separating the variables ๐๐ฆ/๐^4๐ฆ = e3x dx eโ4y dy = e3x dx Integrating both sides โซ1โใ๐^(โ4๐ฆ) ๐๐ฆใ=โซ1โ๐^3๐ฅ ๐๐ฅ ๐^(โ๐๐)/(โ๐)=๐^๐๐/๐+๐ช 0=๐^3๐ฅ/3+๐^(โ4๐ฆ)/4+๐ถ ๐^3๐ฅ/3 + ๐^(โ4๐ฆ)/4 + C = 0 (4๐3๐ฅ" + " 3๐^(โ4๐ฆ))/12 + C = 0 (4๐3๐ฅ" + " 3๐^(โ4๐ฆ) + 12๐ถ)/12 " = 0" ๐๐^๐๐ + ๐๐^(โ๐๐) + 12C = 0 Given y = 0 when x = 0 Putting x = 0 & y = 0 in (1) 4๐^(3(0)) + 3๐^(โ4(0)) + 12C = 0 4๐^0 + 3๐^0 + 12C = 0 4 + 3 + 12C = 0 7 + 12C = 0 12C = โ 7 C = (โ๐)/๐๐ Putting value of C in (1) 4๐^3๐ฅ + 3๐^(โ4๐ฆ) + 12C = 0 4๐^3๐ฅ + 3๐^(โ4๐ฆ) + 12((โ7)/12) = 0 ๐๐^๐๐ + ๐๐^(โ๐๐) โ 7 = 0
Examples
Example 1 (ii) Important
Example 1 (iii) Important
Example 2
Example 3 Important
Example 4
Example 5
Example 6
Example 7 Important
Example 8
Example 9 Important
Example 10 Important
Example 11
Example 12 Important
Example 13 Important
Example 14
Example 15 Important
Example 16
Example 17 Important
Example 18 Important
Example 19
Example 20 You are here
Example 21 Important
Example 22 Important
Question 1
Question 2
Question 3 Important
Question 4
Question 5
Question 6
About the Author
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo